Diego C. Cafaro

Optimal scheduling of multiproduct pipeline systems using a non-discrete MILP formulation

Abstract Multiproduct pipelines permit to transport large volumes of a wide range of refined petroleum products from major supply sources to distribution centers near market areas. Batches of refined products and grades are pumped back-to-back in the same pipeline, often without any separation device between batches. The sequence and lengths of such pumping runs should be carefully selected in order to meet market demands at the promised dates while satisfying many pipeline operational constraints. This paper deals with the scheduling of a multiproduct pipeline system receiving a number of liquid products from a single refinery source to distribute them among several depots. A novel MILP continuous mathematical formulation that neither uses time discretization nor division of the pipeline into a number of single-product packs is presented. By developing a more rigorous problem representation, the quality of the pipeline schedule is significantly improved. Moreover, a severe reduction in binary variables and CPU time with regards to previous approaches is also achieved. To illustrate the proposed approach, a pair of real-world case studies was solved. Both involve the scheduling of a single pipeline carrying four oil derivatives from an oil refinery to five distribution depots. Higher pumping costs at daily peak periods were also considered. Compared with previous work, better solutions were found at much lower computational time.

Dynamic scheduling of multiproduct pipelines with multiple delivery due dates

Abstract Scheduling product batches in pipelines is a very complex task with many constraints to be considered. Several papers have been published on the subject during the last decade. Most of them are based on large-size MILP discrete time scheduling models whose computational efficiency greatly diminishes for rather long time horizons. Recently, an MILP continuous problem representation in both time and volume providing better schedules at much lower computational cost has been published. However, all model-based scheduling techniques were applied to examples assuming a static market environment, a short single-period time horizon and a unique due-date for all deliveries at the horizon end. In contrast, pipeline operators generally use a monthly planning horizon divided into a number of equal-length periods and a cyclic scheduling strategy to fulfill terminal demands at period ends. Moreover, the rerouting of shipments and time-dependent product requirements at distribution terminals force the scheduler to continuously update pipeline operations. To address such big challenges facing the pipeline industry, this work presents an efficient MILP continuous-time framework for the dynamic scheduling of pipelines over a multiperiod moving horizon. At the completion time of the current period, the planning horizon moves forward and the re-scheduling process based on updated problem data is triggered again over the new horizon. Pumping runs may extend over two or more periods and a different sequence of batches may be injected at each one. The approach has successfully solved a real-world pipeline scheduling problem involving the transportation of four products to five destinations over a rolling horizon always comprising four 1-week periods.

Operational scheduling of refined products pipeline networks with simultaneous batch injections

Petroleum refined products are mostly sent from oil refineries to distribution depots by trunk pipelines. Pipeline networks usually involve multiple input and exit terminals, and even dual-purpose stations. Several pumping operations can be simultaneously performed at different sources. Most of the computational burden on the scheduling of multi-source pipeline networks comes from three operational tasks: pump sequencing, batch sizing, and batch allocation. Previous contributions applied discrete decomposition approaches performing such tasks through heuristic-based decisions. This paper introduces an MILP continuous formulation for the operational scheduling of unidirectional pipeline networks that allows simultaneous batch injections. The problem goal is to satisfy depot requirements at minimum total cost. The optimal schedule of pumping and delivery operations is established all at once. Results show that simultaneous batch injections lead to a better use of the pipeline transport capacity and a substantial reduction on the overall time needed to meet depot demands.

MINLP model for the detailed scheduling of refined products pipelines with flow rate dependent pumping costs

Abstract Multiproduct pipelines transport fuels from refineries to distant distribution terminals in batches. The energy needed to move the fluids through the pipeline is mainly associated with elevation gradients and friction head loss. Commonly, friction loss is the major term requiring pump stations to keep the flow moving, and it is strongly dependent on the fluid flow rate. Some studies have been carried out for reducing the pumping costs in multiproduct pipelines, but none of them has been focused on thoroughly considering the head loss due to friction along the pipeline. This paper introduces a novel MINLP continuous-time formulation for the detailed scheduling of single-source pipelines, rigorously tracking power consumption at every pipeline segment through nonlinear equations. Real-world case studies are successfully solved using GAMS–DICOPT algorithm, which proves to be a useful tool for solving large-scale, nonlinear scheduling problems. Important reductions in the operation costs are achieved by keeping a more stable flow rate profile over the planning horizon.

Rigorous scheduling of mesh-structure refined petroleum pipeline networks

Abstract Pipeline networks represent the major mode of transportation for crude oil and refined fuels. Recent data suggest that this trend will persist in coming years. A multiproduct pipeline network can be described as a set of interconnected pipelines with several input and receiving terminals. In the most general case, it has a mesh-like configuration with alternative paths between two terminals. Pumping and delivery operations should be scheduled all at once in an integrated fashion. This work introduces a novel MILP continuous-time formulation for the scheduling of mesh pipeline networks. The pipeline operational plan is conceived as a sequence of composite pumping runs each one involving at most a batch injection at every input station. The model solution simultaneously provides the timing of batch inputs at every source, the product sequence and lot sizes at every pipeline, and the flows diverted to terminals. Three examples of growing complexity were successfully solved at low CPU times.

Rigorous formulation for the scheduling of reversible-flow multiproduct pipelines

Abstract Pipelines play a major role in the petroleum industry by providing a safe, reliable and economical transportation mode over land. Frequently, they connect a pair of refineries or harbors with the purpose of sharing oil products. As the construction of twin pipelines transporting products in opposite directions demands large capital investments, reversible-flow pipelines arise as a promising alternative. This paper introduces a novel continuous-time formulation for the short-term operational planning of reversible multiproduct pipelines. The proposed model allows to change the flow direction as many times as needed to meet terminal demands, determining precise time instants for flow reversals. It provides the input and output schedules in a single step, and the most convenient product used as filler to push current batches out of the line. Three examples are successfully solved with much less computational effort than previous approaches.

Oil-derivatives pipeline logistics using discrete-event simulation

The management of oil-product pipelines represents a critical task in the daily operation of petroleum supply chains. Efficient computational tools are needed to perform this activity in a reliable and costeffective manner. This work presents a novel discrete event simulation system developed on Arena® for the detailed scheduling of a multiproduct pipeline consisting of a sequence of pipes that connect a single input station to several receiving terminals. The pipeline is modeled as a non-traditional multi-server queuing system involving a number of servers at every pipe-end that perform their tasks in a synchronized manner. Based on priority rules, the model decides which server should dispatch the entity waiting for service to the associated depot. Each priority rule can lead to a different delivery schedule, which is evaluated by using several criteria. Combined with optimization tools, the proposed simulation technique permits to easily manage real-world pipelines operations with low computational effort.

Alternate approximation of concave cost functions for process design and supply chain optimization problems

Abstract This short note presents an alternate approximation of concave cost functions used to reflect economies of scale in process design and supply chain optimization problems. To approximate the original concave function, we propose a logarithmic function that is exact and has bounded gradients at zero values in contrast to other approximation schemes. We illustrate the application and advantages of the proposed approximation.

A continuous-time approach to multiproduct pipeline scheduling

Abstract Product distribution planning is a critical stage in oil refinery operation. Pipelines provide the most reliable mode for delivering huge amounts of petroleum products through long distances at low operating cost. In this paper, the short-term scheduling of a multiproduct pipeline receiving a number of liquid products from a single refinery source to distribute them among several depots has been studied. The pipeline operation usually implies to accomplish a sequence of product pumping runs of suitable length in order to meet customer demands at the promised dates while satisfying all operational constraints. This work introduces a novel MILP mathematical formulation that neither uses time discretization nor division of the pipeline into a number of single-product packs. In this way, a more rigorous problem representation ensuring the optimality of the proposed schedule has been developed. Moreover, a severe reduction in binary variables and CPU time with regards to previous approaches was also achieved. A realworld case study involving a single pipeline, four oil products and five distribution depots was successfully solved.

Optimization Models for Optimal Investment, Drilling, and Water Management in Shale Gas Supply Chains

Abstract This paper provides an overview of recent optimization models for shale gas production. We first describe a new mixed-integer optimization model for the design of shale gas infrastructures. It is aimed at optimizing the number of wells to drill, size and location of new gas processing plants, section and length of pipelines for gathering raw gas, delivering dry gas and natural gas liquids, power of gas compressors, and planning of freshwater consumption for well drilling and fracturing. We also describe a detailed operational mixed-integer linear model to optimize life cycle water use for well pads. The objective of the model is to determine the fracturing schedule that minimizes costs for freshwater consumption, transportation, treatment, storage, and disposal.